Walcott did not have time to say his goodbyes to his team-mates and the staff at the north London club, who he joined at the age of 16.
Now 28, the England international has accepted a new challenge under Sam Allardyce at Goodison Park, completing his £20m move earlier this week.
“When I found I was coming here I had to go there at night and pick up my stuff in bin bags,” Walcott said. “I’m sure I’ll get some time to go down. I’ve had so many messages to try and catch up with people.
“It’s been overwhelming but I’m slowly but surely going through those messages and I will at some point go back there and say my proper goodbyes.”
Southampton, Walcott’s former club, were also interested in taking him from Arsenal, but the advice of former international team-mate Wayne Rooney helped Everton win the race for his signature.
When asked what Rooney had said to him to convince him to join, Walcott replied: “He said all the golf courses are great!
“I played a lot of football with Wayne and I just wanted to get a structure of how the club worked and what the players are like.
“When you’re used to something for so long, it’s a big decision to change things but I felt it was the right decision to do that.
“I got a sense from Wayne he was hungry, eager to push on. He felt like this was the right place. It was a long process but we’re here in the end now.”
Walcott is yet to start a Premier League game this season having fallen out of favour at the Emirates under Arsene Wenger, but the 28-year-old insisted on Friday that he still retains maximum respect for his former manager.
“With any player, if you’re not playing you would be upset but you have to dig deep and try to push to get into the position. For whatever reason it did not happen this year, that’s why I’ve moved on.
“I was there since I was 16 and to bring in a young player and have belief in him, like I say, I can’t thank him enough. Now I’ve got a new challenge, a new manager I want to impress and get the ball rolling.”